{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用最小二乘法拟和曲线\n",
    "\n",
    "高斯于1823年在误差$e_1,…,e_n$独立同分布的假定下,证明了最小二乘方法的一个最优性质: 在所有无偏的线性估计类中,最小二乘方法是其中方差最小的！\n",
    "对于数据$(x_i, y_i)   (i=1, 2, 3...,m)$\n",
    "\n",
    "拟合出函数$h(x)$\n",
    "\n",
    "有误差，即残差：$r_i=h(x_i)-y_i$\n",
    "\n",
    "此时$L2$范数(残差平方和)最小时，$h(x)$ 和 $y$ 相似度最高，更拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一般的$H(x)$为$n$次的多项式，$H(x)=w_0+w_1x+w_2x^2+...w_nx^n$\n",
    "\n",
    "$w(w_0,w_1,w_2,...,w_n)$为参数\n",
    "\n",
    "最小二乘法就是要找到一组 $w(w_0,w_1,w_2,...,w_n)$ ，使得$\\sum_{i=1}^n(h(x_i)-y_i)^2$ (残差平方和) 最小\n",
    "\n",
    "即，求 $min\\sum_{i=1}^n(h(x_i)-y_i)^2$\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.optimize import leastsq\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 函数调用说明 numpy.poly1d([1,2,3])  生成  $1x^2+2x^1+3x^0$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 目标函数𝑦=𝑠𝑖𝑛2𝜋𝑥——在几个频率值下测试：1,2,3,9\n",
    "def real_func(x):\n",
    "    #return np.sin(2*np.pi*x)\n",
    "    #return np.sin(2*2*np.pi*x)\n",
    "    return np.sin(4*2*np.pi*x)\n",
    "    #return np.sin(8*2*np.pi*x)\n",
    "\n",
    "# 多项式\n",
    "def fit_func(p, x):\n",
    "    f = np.poly1d(p)\n",
    "    return f(x)\n",
    "\n",
    "# 残差\n",
    "def residuals_func(p, x, y):\n",
    "    ret = fit_func(p, x) - y\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 调整数据点数，进行测试\n",
    "#x = np.linspace(0, 1, 10)\n",
    "#x = np.linspace(0, 1, 100)\n",
    "x = np.linspace(0, 1, 200)\n",
    "\n",
    "x_points = np.linspace(0, 1, 1000)\n",
    "# 加上正态分布噪音的目标函数的值——在几个噪声方差上进行测试\n",
    "y_ = real_func(x)\n",
    "#y = [np.random.normal(0, 0.1) + y1 for y1 in y_]\n",
    "y = [np.random.normal(0, 0.2) + y1 for y1 in y_]\n",
    "#y = [np.random.normal(0, 0.3) + y1 for y1 in y_]\n",
    "#y = [np.random.normal(0, 0.5) + y1 for y1 in y_]\n",
    "\n",
    "\n",
    "\n",
    "def fitting(M=0):\n",
    "    \"\"\"\n",
    "    M    为 多项式的次数\n",
    "    \"\"\"\n",
    "    # 随机初始化多项式参数\n",
    "    p_init = np.random.rand(M + 1)\n",
    "    # 最小二乘法\n",
    "    p_lsq = leastsq(residuals_func, p_init, args=(x, y))\n",
    "    print('Fitting Parameters:', p_lsq[0])\n",
    "\n",
    "    # 可视化\n",
    "    plt.plot(x_points, real_func(x_points), label='real')\n",
    "    plt.plot(x_points, fit_func(p_lsq[0], x_points), label='fitted curve')\n",
    "    plt.plot(x, y, 'bo', label='noise')\n",
    "    plt.legend()\n",
    "    return p_lsq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-6.67814635e+03  1.00648512e+05 -3.73682293e+05  6.55966332e+05\n",
      " -6.50178606e+05  3.87588932e+05 -1.40097291e+05  2.95781277e+04\n",
      " -3.29372154e+03  1.49925247e+02 -9.02884346e-01]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=10\n",
    "p_lsq_0 = fitting(M=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-5.96136491e+04  2.99917900e+05 -4.67776393e+04  7.98384244e+05\n",
      " -2.74454436e+06 -1.24619877e+06  4.75515607e+06  5.28942494e+05\n",
      " -2.76903048e+05 -2.23907282e+06 -3.32155910e+05 -2.41775613e+06\n",
      "  9.95143659e+05  2.22986522e+06  2.06984829e+06  6.47825559e+05\n",
      " -2.33515617e+06 -2.82885386e+06 -1.53146392e+06  4.88444753e+06\n",
      "  2.03988634e+06 -3.34528115e+06 -2.41852720e+06  4.14905038e+06\n",
      " -1.88300006e+06  2.97550066e+05  1.80454915e+04 -9.34742185e+03\n",
      "  5.82142216e+02  6.49159818e+00  1.90553327e-01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=30\n",
    "p_lsq_1 = fitting(M=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-4.85798793e+05  1.54828038e+06 -4.87773558e+05 -4.57439550e+05\n",
      " -1.13129101e+06 -2.46976058e+05  1.95706434e+05  1.02638092e+06\n",
      "  8.47175093e+05 -2.51209262e+05  4.39332532e+05  1.38798857e+05\n",
      "  1.44500855e+05 -1.27347936e+06 -1.35283725e+06 -1.50301555e+05\n",
      "  1.17292143e+06  3.05098107e+05 -2.38586121e+05 -3.30844629e+05\n",
      "  6.31821885e+05  1.59837177e+04  7.68440226e+03  8.23729387e+05\n",
      " -1.95843068e+02  1.31168745e+05 -4.30221369e+05 -1.16954237e+06\n",
      " -3.66104084e+05 -1.30894324e+05  2.53893594e+04  4.71599944e+05\n",
      "  1.04078016e+06  7.88742836e+05  5.03538274e+05 -1.27697699e+06\n",
      " -1.70876210e+06 -7.36247960e+04  7.07264990e+05  1.29381265e+06\n",
      "  4.12170122e+05 -1.16894766e+06 -8.29016239e+05  1.15091550e+06\n",
      " -8.96816473e+04 -2.78789212e+05  1.26307028e+05 -2.10463517e+04\n",
      "  1.24542496e+03 -9.29553451e+00  2.71906638e-01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=50\n",
    "p_lsq_3 = fitting(M=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [ 5.16432747e+04  2.23046183e+04 -1.88831270e+04  1.26960815e+03\n",
      " -2.74908623e+04 -7.93346112e+04  2.46784609e+04  9.78508120e+03\n",
      "  3.59437046e+03  3.90367093e+04 -2.76461998e+04  1.76442900e+04\n",
      " -1.17683252e+05 -4.74756741e+04  2.64252945e+04 -5.49772274e+04\n",
      "  5.95703554e+04  3.06188293e+03  6.58297049e+03 -1.41127013e+04\n",
      "  4.61094661e+04  2.89677394e+04  2.11645193e+04  2.01184741e+04\n",
      " -2.99768430e+04 -2.81149213e+04  8.83131737e+04 -7.36500708e+04\n",
      "  1.00414316e+05  3.14402248e+04  2.51088731e+04  4.59166783e+04\n",
      " -9.44012106e+03  1.66898163e+04  7.34711990e+04 -2.53580537e+04\n",
      " -2.09089741e+04 -8.86306165e+04  3.74410503e+04  1.10948506e+05\n",
      " -3.31413410e+04 -6.56785427e+04  1.05877456e+05  1.33578910e+04\n",
      " -3.57904582e+04 -3.22530523e+04 -1.92769615e+04 -1.08391780e+05\n",
      " -2.97160758e+04 -6.73033476e+04 -1.64802056e+04 -9.25911048e+04\n",
      " -1.73935258e+04 -1.66388100e+05  1.99200882e+04  7.33369986e+04\n",
      " -3.76321610e+03 -4.70195313e+04 -3.53876353e+04 -3.60390502e+04\n",
      "  3.27902481e+04 -7.92808033e+03  3.41076845e+04  4.61984810e+04\n",
      "  3.01683772e+04  3.47888912e+04  1.19573350e+04  6.81162446e+04\n",
      "  5.28766895e+04 -4.05763414e+04  7.81190060e+04 -1.00602150e+04\n",
      "  6.73866587e+04 -6.73032348e+04 -1.04604771e+04 -3.14181136e+04\n",
      "  1.31990920e+05 -1.47352815e+04 -5.00709369e+04  1.92458123e+05\n",
      "  5.46889432e+04  4.73202779e+04  2.37406974e+04 -1.48784124e+04\n",
      " -1.59896792e+04 -5.54613357e+04 -1.79331469e+04 -9.34470175e+03\n",
      "  3.89386860e+04  6.25358648e+03 -3.34155535e+04  1.04687791e+04\n",
      " -3.20436651e+04 -2.50125735e+04 -1.01801148e+05  3.62087653e+04\n",
      " -7.83652044e+04  6.85151134e+03 -8.53040041e+04 -7.16879577e+04\n",
      " -8.44063825e+04  9.13482154e+03  4.23661667e+03 -3.57904667e+04\n",
      " -6.93483980e+04 -4.14336491e+04 -2.56533436e+04  3.72630447e+03\n",
      " -2.51179020e+04  2.28229264e+04  4.46121212e+04  4.21222750e+04\n",
      "  3.86443876e+04  5.15139406e+04  6.44739240e+04  3.84685000e+04\n",
      "  4.79279372e+04  9.04644205e+04  1.02689127e+05  1.36625235e+05\n",
      "  4.26834106e+03  8.24333326e+04  4.31378146e+04 -2.41199331e+04\n",
      " -2.44810509e+04 -1.36257409e+04 -3.47259426e+04 -7.38952787e+04\n",
      " -8.35859519e+04 -1.02439965e+05 -1.17433116e+05 -1.10144210e+05\n",
      "  1.65141712e+04 -7.55403590e+04  6.28388432e+04 -5.66367089e+04\n",
      " -6.87016359e+04 -5.32068757e+04 -2.13866230e+04  4.61764647e+03\n",
      "  6.12005942e+04  5.72061004e+04  9.93432861e+04  1.03409524e+05\n",
      "  1.33250589e+05  1.06851388e+05  1.29892538e+05  5.75768731e+04\n",
      "  2.65229686e+04 -4.08294389e+04 -9.63234703e+04 -1.41227529e+05\n",
      " -1.74106674e+05 -1.81194397e+05 -1.03396438e+05 -8.80291789e+04\n",
      "  4.08600191e+03  5.87373886e+04  1.44577853e+05  1.96167831e+05\n",
      "  2.05649237e+05  1.60809170e+05  3.12923051e+04 -1.17385410e+05\n",
      " -2.36759865e+05 -2.60189916e+05 -1.55923986e+05  5.03595634e+04\n",
      "  2.51384223e+05  2.92274869e+05  8.74864498e+04 -2.61951887e+05\n",
      " -3.09929245e+05  1.26586364e+05  3.59678099e+05 -3.25239034e+05\n",
      "  1.07235040e+05 -1.48241915e+04  5.80787623e+02  1.61826450e+01\n",
      "  6.93861157e-02]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=180\n",
    "p_lsq_9 = fitting(M=180)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 正则化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "结果显示过拟合， 引入正则化项(regularizer)，降低过拟合\n",
    "\n",
    "$Q(x)=\\sum_{i=1}^n(h(x_i)-y_i)^2+\\lambda||w||^2$。\n",
    "\n",
    "回归问题中，损失函数是平方损失，正则化可以是参数向量的L2范数,也可以是L1范数。\n",
    "\n",
    "- L1: regularization\\*abs(p)\n",
    "\n",
    "- L2: 0.5 \\* regularization \\* np.square(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "regularization = 0.0001\n",
    "\n",
    "\n",
    "def residuals_func_regularization(p, x, y):\n",
    "    ret = fit_func(p, x) - y\n",
    "    ret = np.append(ret,\n",
    "                    np.sqrt(0.5 * regularization * np.square(p)))  # L2范数作为正则化项\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 最小二乘法,加正则化项\n",
    "p_init = np.random.rand(9 + 1)\n",
    "p_lsq_regularization = leastsq(\n",
    "    residuals_func_regularization, p_init, args=(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x8f18388>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_points, real_func(x_points), label='real')\n",
    "plt.plot(x_points, fit_func(p_lsq_9[0], x_points), label='fitted curve')\n",
    "plt.plot(\n",
    "    x_points,\n",
    "    fit_func(p_lsq_regularization[0], x_points),\n",
    "    label='regularization')\n",
    "plt.plot(x, y, 'bo', label='noise')\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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